Re: Functions with parameters?

*To*: mathgroup at smc.vnet.net*Subject*: [mg22252] Re: [mg22214] Functions with parameters?*From*: BobHanlon at aol.com*Date*: Sat, 19 Feb 2000 01:33:55 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

f[x_, a_] := Log[x/(x - a)] Off[Plot3D::gval]; Off[Power::infy]; Off[Plot3D::plnc]; The function will have a discontinuity (i.e., not be defined) when x = a. Plot3D[Abs[f[x, a]], {x, -5, 5}, {a, -5, 5}, PlotPoints -> 20]; Plot3D[Re[f[x, a]], {x, -5, 5}, {a, -5, 5}, PlotPoints -> 20]; Plot3D[Im[f[x, a]], {x, -5, 5}, {a, -5, 5}, PlotPoints -> 20]; For the function to have real values, the argument of the Log must be positive Needs["Algebra`InequalitySolve`"] InequalitySolve[x/(x - a) > 0, {x, a}] x < 0 && a > x || x > 0 && a < x Since you also specified that a is positive InequalitySolve[x/(x - a) > 0 && a > 0, {x, a}] x < 0 && a > 0 || x > 0 && 0 < a < x Plot3D[f[x, a], {x, -5, 5}, {a, 0, 5}, PlotPoints -> 20]; For the derivative g[x_, a_] := Evaluate[D[f[x, a], x] // Simplify // Factor] g[x, a] a/((a - x)*x) The derivative has discontinuities at x = 0 and x = a. Draw the graphs as above for g[x, a]. Bob Hanlon In a message dated 2/18/2000 4:02:56 AM, tautenhahn at fichtelgebirge.org writes: >I have Mathematica 4 and I want to discuss a simple function with a >parameter; The problem, however, is that I neither found some help in >the online help of Mathematica nor in the book (which is about >Mathematica 3) by Michael Kofler. >I don't know if it is possible to do everything I want to do with >Mathematica and that's why I'm asking here. >The function I want to discuss is > >f(x)=ln(x/(x-a) with a>0 >ok, in Mathematica you type f[x_]=Log[x/(x-a)]. >what I want to do is: > >* where is this function defined (I don't know if this is the right >English word; for example 1/x is *not* defined for x=0; i hope you >understand what I mean); > >* derivatives etc. --> no problem, but again: where is f'(x) defined? > >* Plot the function for several values of a >